Investigation of compressible flow under low Mach number in an enclosed square cavity with a novel non-Boussinesq algorithm

Natural convection is widely observed in various scales of natural phenomena and industrial applications. The low Mach number (i.e., low-velocity) natural convection, especially under large temperature differences and significant density and pressure fluctuations, is of great research significance in industrial fields such as nuclear engineering. The Boussinesq approximation based on the incompressible Navier-Stokes (NS) equation is not fully descriptive due to the neglect of coupling effects among temperature, density, and pressure. As for numerical algorithms based on the compressible Navier-Stokes equation, they often suffer from high computational costs and convergence difficulties. In this paper, a novel numerical algorithm based on the decoupled and stabilized Lattice Boltzmann multiphase model with a complete physical description and clear conceptual framework is proposed. It couples the equation of state and the temperature equation, considering the full effects of gravity, pressure, and temperature-dependent density on flow disturbances, and it recovers the complete compressible NS equation. Taking the natural convection in an enclosed cavity as an example, the non-dimensional numbers governing the fluid system are identified by Buckingham pi theorem; thus, a new thermal expansion number is proposed to connect the pressure effect. The accuracy and reliability of the numerical algorithm are validated by comparing it with standard benchmarks. On this basis, the proposed algorithm enables a unified physical description from low to high Rayleigh numbers and from small to large temperature differences. By analyzing the flow and heat transfer characteristics of natural convection under different Rayleigh numbers, temperature differences, and thermal expansion numbers, this study reveals the coupled physical mechanisms of low Mach number flow from small to large temperature differences, from low to high Rayleigh numbers and under different thermal expansion numbers.